diff --git a/src/Runtime/Core/Maths/Region.cs b/src/Runtime/Core/Maths/Region.cs
index 4868256b..f9398a1c 100644
--- a/src/Runtime/Core/Maths/Region.cs
+++ b/src/Runtime/Core/Maths/Region.cs
@@ -4,6 +4,7 @@
 
 namespace Microsoft.ML.Probabilistic.Math
 {
+    using Microsoft.ML.Probabilistic.Utilities;
     using System;
 
     /// <summary>
@@ -11,7 +12,7 @@ namespace Microsoft.ML.Probabilistic.Math
     /// </summary>
     public class Region
     {
-        public Vector Lower, Upper;
+        public readonly Vector Lower, Upper;
 
         public int Dimension
         {
@@ -113,5 +114,35 @@ namespace Microsoft.ML.Probabilistic.Math
         {
             return string.Format("[{0},{1}]", Lower.ToString(format), Upper.ToString(format));
         }
+
+        public override bool Equals(object obj)
+        {
+            Region that = obj as Region;
+            if (that == null) return false;
+            return (that.Lower == this.Lower) && (that.Upper == this.Upper);
+        }
+
+        public override int GetHashCode()
+        {
+            return Hash.Combine(Lower.GetHashCode(), Upper.GetHashCode());
+        }
+
+        public int CompareTo(Region other)
+        {
+            int result = CompareTo(Lower, other.Lower);
+            if (result == 0) result = CompareTo(Upper, other.Upper);
+            return result;
+        }
+
+        public int CompareTo(Vector a, Vector b)
+        {
+            int result = 0;
+            for (int i = 0; i < a.Count; i++)
+            {
+                result = a[i].CompareTo(b[i]);
+                if (result != 0) return result;
+            }
+            return result;
+        }
     }
 }
diff --git a/src/Runtime/Distributions/InnerQuantiles.cs b/src/Runtime/Distributions/InnerQuantiles.cs
index 96f9f9c6..2dd31d3d 100644
--- a/src/Runtime/Distributions/InnerQuantiles.cs
+++ b/src/Runtime/Distributions/InnerQuantiles.cs
@@ -33,6 +33,8 @@ namespace Microsoft.ML.Probabilistic.Distributions
         {
             if (quantiles == null) throw new ArgumentNullException(nameof(quantiles));
             if (quantiles.Length == 0) throw new ArgumentException("quantiles array is empty", nameof(quantiles));
+            OuterQuantiles.AssertFinite(quantiles, nameof(quantiles));
+            OuterQuantiles.AssertNondecreasing(quantiles, nameof(quantiles));
             this.quantiles = quantiles;
             lowerGaussian = GetLowerGaussian(quantiles);
             upperGaussian = GetUpperGaussian(quantiles);
diff --git a/src/Runtime/Distributions/IrregularQuantiles.cs b/src/Runtime/Distributions/IrregularQuantiles.cs
new file mode 100644
index 00000000..52a5bc0a
--- /dev/null
+++ b/src/Runtime/Distributions/IrregularQuantiles.cs
@@ -0,0 +1,106 @@
+using Microsoft.ML.Probabilistic.Math;
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace Microsoft.ML.Probabilistic.Distributions
+{
+    /// <summary>
+    /// Represents a distribution using the quantiles at arbitrary probabilities.
+    /// </summary>
+    public class IrregularQuantiles : CanGetQuantile, CanGetProbLessThan
+    {
+        /// <summary>
+        /// Sorted in ascending order.
+        /// </summary>
+        private readonly double[] probabilities, quantiles;
+
+        public IrregularQuantiles(double[] probabilities, double[] quantiles)
+        {
+            AssertIncreasing(probabilities, nameof(probabilities));
+            AssertInRange(probabilities, nameof(probabilities));
+            OuterQuantiles.AssertNondecreasing(quantiles, nameof(quantiles));
+            OuterQuantiles.AssertFinite(quantiles, nameof(quantiles));
+            this.probabilities = probabilities;
+            this.quantiles = quantiles;
+        }
+
+        private void AssertIncreasing(double[] array, string paramName)
+        {
+            for (int i = 1; i < array.Length; i++)
+            {
+                if (array[i] <= array[i - 1]) throw new ArgumentException($"Array is not increasing: {paramName}[{i}] {array[i]} <= {paramName}[{i - 1}] {array[i - 1]}", paramName);
+            }
+        }
+
+        private static void AssertInRange(double[] array, string paramName)
+        {
+            for (int i = 0; i < array.Length; i++)
+            {
+                if (array[i] < 0) throw new ArgumentOutOfRangeException(paramName, $"{paramName}[{i}] {array[i]} < 0");
+                if (array[i] > 1) throw new ArgumentOutOfRangeException(paramName, $"{paramName}[{i}] {array[i]} > 1");
+                if (double.IsNaN(array[i])) throw new ArgumentOutOfRangeException(paramName, $"{paramName}[{i}] {array[i]}");
+            }
+        }
+
+        /// <summary>
+        /// Returns the quantile rank of x.  This is a probability such that GetQuantile(probability) == x, whenever x is inside the support of the distribution.  May be discontinuous due to duplicates.
+        /// </summary>
+        /// <param name="x"></param>
+        /// <returns>A real number in [0,1]</returns>
+        public double GetProbLessThan(double x)
+        {
+            int index = Array.BinarySearch(quantiles, x);
+            if (index >= 0)
+            {
+                // In case of duplicates, find the smallest copy.
+                while (index > 0 && quantiles[index - 1] == x) index--;
+                return probabilities[index];
+            }
+            else
+            {
+                // Linear interpolation
+                int largerIndex = ~index;
+                if (largerIndex == 0) return 0;
+                if (largerIndex == quantiles.Length) return 1;
+                int smallerIndex = largerIndex - 1;
+                double slope = (quantiles[largerIndex] - quantiles[smallerIndex]) / (probabilities[largerIndex] - probabilities[smallerIndex]);
+                return probabilities[smallerIndex] + (x - quantiles[smallerIndex]) / slope;
+            }
+        }
+
+        /// <summary>
+        /// Returns the largest value x such that GetProbLessThan(x) &lt;= probability.
+        /// </summary>
+        /// <param name="probability">A real number in [0,1].</param>
+        /// <returns></returns>
+        public double GetQuantile(double probability)
+        {
+            if (probability < 0) throw new ArgumentOutOfRangeException(nameof(probability), "probability < 0");
+            if (probability > 1.0) throw new ArgumentOutOfRangeException(nameof(probability), "probability > 1.0");
+            // The zero-based index of item in the sorted List<T>, if item is found; 
+            // otherwise, a negative number that is the bitwise complement of the index of the next element that is larger than item 
+            // or, if there is no larger element, the bitwise complement of Count.
+            int index = Array.BinarySearch(probabilities, probability);
+            if(index >= 0)
+            {
+                return quantiles[index];
+            }
+            else
+            {
+                // Linear interpolation
+                int largerIndex = ~index;
+                if (largerIndex == 0) return quantiles[largerIndex];
+                int smallerIndex = largerIndex - 1;
+                if (largerIndex == probabilities.Length) return quantiles[smallerIndex];
+                double slope = (quantiles[largerIndex] - quantiles[smallerIndex]) / (probabilities[largerIndex] - probabilities[smallerIndex]);
+                // Solve for the largest x such that probabilities[smallerIndex] + (x - quantiles[smallerIndex]) / slope <= probability.
+                double frac = MMath.LargestDoubleSum(-probabilities[smallerIndex], probability);
+                double offset = MMath.LargestDoubleProduct(slope, frac);
+                return MMath.LargestDoubleSum(quantiles[smallerIndex], offset);
+            }
+        }
+    }
+}
diff --git a/src/Runtime/Distributions/OuterQuantiles.cs b/src/Runtime/Distributions/OuterQuantiles.cs
index c8d914be..732ca3f9 100644
--- a/src/Runtime/Distributions/OuterQuantiles.cs
+++ b/src/Runtime/Distributions/OuterQuantiles.cs
@@ -19,13 +19,32 @@ namespace Microsoft.ML.Probabilistic.Distributions
         /// <summary>
         /// Numbers in increasing order.
         /// </summary>
-        private double[] quantiles;
+        private readonly double[] quantiles;
 
         public OuterQuantiles(double[] quantiles)
         {
+            AssertNondecreasing(quantiles, nameof(quantiles));
+            AssertFinite(quantiles, nameof(quantiles));
             this.quantiles = quantiles;
         }
 
+        internal static void AssertFinite(double[] array, string paramName)
+        {
+            for (int i = 0; i < array.Length; i++)
+            {
+                if (double.IsInfinity(array[i])) throw new ArgumentOutOfRangeException(paramName, $"{paramName}[{i}] {array[i]}");
+                if (double.IsNaN(array[i])) throw new ArgumentOutOfRangeException(paramName, $"{paramName}[{i}] {array[i]}");
+            }
+        }
+
+        internal static void AssertNondecreasing(double[] array, string paramName)
+        {
+            for (int i = 1; i < array.Length; i++)
+            {
+                if (array[i] < array[i - 1]) throw new ArgumentException($"Array is not non-decreasing: {paramName}[{i}] {array[i]} < {paramName}[{i - 1}] {array[i - 1]}", paramName);
+            }
+        }
+
         public OuterQuantiles(int quantileCount, CanGetQuantile canGetQuantile)
         {
             this.quantiles = new double[quantileCount];
@@ -99,7 +118,7 @@ namespace Microsoft.ML.Probabilistic.Distributions
             double pos = MMath.LargestDoubleProduct(n - 1, probability);
             int lower = (int)Math.Floor(pos);
             if (lower == n - 1) return quantiles[lower];
-            return GetQuantile(probability, lower, quantiles[lower], quantiles[lower+1], n);
+            return GetQuantile(probability, lower, quantiles[lower], quantiles[lower + 1], n);
         }
 
         /// <summary>
diff --git a/test/Tests/BlogTests.cs b/test/Tests/BlogTests.cs
index fae4ee76..47536bfb 100644
--- a/test/Tests/BlogTests.cs
+++ b/test/Tests/BlogTests.cs
@@ -2317,7 +2317,8 @@ namespace Microsoft.ML.Probabilistic.Tests
             Console.WriteLine("P(woman's height|isTaller) = {0}", engine.Infer(heightWoman));
         }
 
-        internal void Handedness()
+        [Fact]
+        public void Handedness()
         {
             bool[] studentData = {false, true, true, true, true, true, true, true, false, false};
             bool[] lecturerData = {false, true, true, true, true, true, true, true, true, true};
@@ -2339,7 +2340,9 @@ namespace Microsoft.ML.Probabilistic.Tests
             // -----------------------------------
             InferenceEngine engine = new InferenceEngine();
             //Console.WriteLine("isRightHanded = {0}", engine.Infer(isRightHanded));
-            Console.WriteLine("probRightHanded = {0}", engine.Infer(probRightHanded));
+            var probRightHandedExpected = new Beta(7.72, 3.08);
+            var probRightHandedActual = engine.Infer<Beta>(probRightHanded);
+            Assert.True(probRightHandedExpected.MaxDiff(probRightHandedActual) < 1e-4);
         }
 
         [Fact]
diff --git a/test/Tests/DiscreteTests.cs b/test/Tests/DiscreteTests.cs
index 46ddc051..7733cf36 100644
--- a/test/Tests/DiscreteTests.cs
+++ b/test/Tests/DiscreteTests.cs
@@ -85,6 +85,7 @@ namespace Microsoft.ML.Probabilistic.Tests
             VariableArray<bool> observedBlue = Variable.Array<bool>(draw).Named("observedBlue");
             using (Variable.ForEach(draw))
             {
+                // cannot use Variable.DiscreteUniform(numBalls) here since ballIndex will get the wrong range.
                 Variable<int> ballIndex = Variable.DiscreteUniform(ball, numBalls).Named("ballIndex");
                 using (Variable.Switch(ballIndex))
                 {
@@ -100,10 +101,10 @@ namespace Microsoft.ML.Probabilistic.Tests
             // 16 iters with good schedule
             // 120 iters with bad schedule
             engine.NumberOfIterations = 150;
-            Discrete numUsersActual = engine.Infer<Discrete>(numBalls);
-            Console.WriteLine("numBalls = {0}", numUsersActual);
-            Discrete numUsersExpected = new Discrete(0, 0.5079, 0.3097, 0.09646, 0.03907, 0.02015, 0.01225, 0.008336, 0.006133);
-            Assert.True(numUsersExpected.MaxDiff(numUsersActual) < 1e-4);
+            Discrete numBallsActual = engine.Infer<Discrete>(numBalls);
+            Console.WriteLine("numBalls = {0}", numBallsActual);
+            Discrete numBallsExpected = new Discrete(0, 0.5079, 0.3097, 0.09646, 0.03907, 0.02015, 0.01225, 0.008336, 0.006133);
+            Assert.True(numBallsExpected.MaxDiff(numBallsActual) < 1e-4);
             numBalls.ObservedValue = 1;
             Console.WriteLine(engine.Infer(isBlue));
         }
diff --git a/test/Tests/Properties/AssemblyInfo.cs b/test/Tests/Properties/AssemblyInfo.cs
index ea12f586..067fe854 100644
--- a/test/Tests/Properties/AssemblyInfo.cs
+++ b/test/Tests/Properties/AssemblyInfo.cs
@@ -9,7 +9,7 @@ using System.Runtime.InteropServices;
 // set of attributes. Change these attribute values to modify the information
 // associated with an assembly.
 
-[assembly: AssemblyTitle("Infer2Tests")]
+[assembly: AssemblyTitle("Microsoft.ML.Probabilistic.Tests")]
 [assembly: AssemblyDescription("")]
 [assembly: AssemblyConfiguration("")]
 [assembly: AssemblyCompany("Microsoft Research Limited")]
diff --git a/test/Tests/QuantileTests.cs b/test/Tests/QuantileTests.cs
index 1462839e..10e275e4 100644
--- a/test/Tests/QuantileTests.cs
+++ b/test/Tests/QuantileTests.cs
@@ -16,6 +16,26 @@ namespace Microsoft.ML.Probabilistic.Tests
 
     public class QuantileTests
     {
+        [Fact]
+        public void IrregularQuantilesTest()
+        {
+            var iq = new IrregularQuantiles(new double[] { 0, 0.4, 1 }, new double[] { 3, 4, 5 });
+            Assert.Equal(3.25, iq.GetQuantile(0.1));
+            Assert.Equal(0.1, iq.GetProbLessThan(3.25));
+            CheckGetQuantile(iq, iq);
+        }
+
+        [Fact]
+        public void IrregularQuantiles_InfinityTest()
+        {
+            Assert.Throws<ArgumentOutOfRangeException>(() =>
+            {
+                var iq = new IrregularQuantiles(new double[] { 0, 0.4, 1 }, new double[] { double.NegativeInfinity, 4, double.PositiveInfinity });
+                Assert.Equal(3.25, iq.GetQuantile(0.1));
+                Assert.Equal(0.1, iq.GetProbLessThan(3.25));
+            });
+        }
+
         [Fact]
         public void QuantileEstimator_SinglePointIsMedian()
         {
@@ -279,11 +299,11 @@ namespace Microsoft.ML.Probabilistic.Tests
             foreach(double maximumError in new[] { 0.05, 0.01, 0.005, 0.001 })
             {
                 int n = (int)(2.0 / maximumError);
-                QuantileEstimator(maximumError, n);
+                QuantileEstimatorTester(maximumError, n);
             }
         }
 
-        private void QuantileEstimator(double maximumError, int n)
+        private void QuantileEstimatorTester(double maximumError, int n)
         {
             // draw many samples from N(m,v)
             Rand.Restart(0);